A generalization of twistor lines for complex tori

Abstract

In this work we generalize the classical notion of a (compact) twistor line in the period domain of compact complex tori. We introduce two new types of lines, which are non-compact analytic curves in the period domain of complex tori. We study the analytic properties of the compactifications of the curves, the preservation of cohomology classes of type (1,1) along the curves and the twistor path connectivity of the period domain by the curves of one of the new types.